# Assessment of Bayesian Changepoint Detection Methods for Soil Layering Identification Using Cone Penetration Test Data

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Offline BCPD

#### Maximum a Posteriori Estimations of Changepoints

#### 2.2. Online BCPD

#### Maximum a Posteriori Estimations of Changepoints

#### 2.3. CPT Data Case Study

#### 2.4. Priors for Univariate and Multivariate BCPD Methods

#### 2.5. Performance Metrics

- True Positive (TP)—the number of times the method has correctly identified a soil layer boundary;
- False Positive (FP)—the number of times the method has incorrectly identified a soil layer boundary;
- False Negative (FN)—the number of times the method has failed to identify a true soil layer boundary;
- Precision = TP/(TP + FP);
- Sensitivity = TP/(TP + FN);
- F1 score = 2(Precision × Sensitivity)/(Precision + Sensitivity).

## 3. Results

#### Comparison of Performance Metrics

## 4. Discussion

## 5. Conclusions

- Univariate BCPD methods (using ${I}_{c}$ data) are generally more accurate and computationally efficient than their multivariate counterparts (using ${Q}_{t}$ and ${F}_{r}$ data) in identifying soil layer boundaries using CPT data.
- The newly developed univariate online BCPD method demonstrates the highest accuracy and computational efficiency.
- This research underscores the advantage of unsupervised BCPD methods, which forego the need for training data and manual analysis, contributing to the advancement of fast, automated Bayesian geotechnical analysis techniques.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of a series of data points (shown as grey markers). There are three distinct partitions in the data series, separated by changepoints. The changepoints are detected at locations where abrupt changes are observed.

**Figure 2.**Illustration of the development of the most probable ${r}_{z}$ for a sequence of data (shown in bottom subfigure) and how the changepoints coincide with the locations where the most probable ${r}_{z}$ is 0. Here, $y$ is the measured quantity and $z$ is depth (for depth series data). The dashed lines represent the known locations of the changepoints.

**Figure 3.**Workflow summarising the steps from the raw CPT measurements to the soil layer boundary predictions by the univariate and multivariate BCPD methods.

**Figure 4.**Comparison of the best-fit inverse gamma cumulative distribution with the actual cumulative distribution of the variance in the CPT ${I}_{c}$ data within each soil layer (known from the borehole data).

**Figure 5.**Comparison of soil layer boundary predictions by the different BCPD methods (shown as horizontal black lines) with the corresponding Robertson (2009) predictions (labelled as ‘ROB’) and ground truth provided by neighbouring borehole data (labelled as ‘BH’), at location CPT01. Fine- and coarse-grained soils are shown as light and dark grey colours, respectively.

SBT Zone | I_{c} Range | Soil Mixture Description |
---|---|---|

9 | - | Stiff fine grained |

8 | - | Stiff sand to clayey sand |

7 | <1.31 | Gravelly sand to dense sand |

6 | 1.31–2.05 | Clean sand to silty sand |

5 | 2.05–2.6 | Silty sand to sandy silt |

4 | 2.6–2.95 | Clayey silt to silty clay |

3 | 2.95–3.6 | Silty clay to clay |

2 | >3.6 | Organic soils |

1 | - | Sensitive soils |

Method | True Positive | False Positive | False Negative | Precision | Sensitivity | F1 Score |
---|---|---|---|---|---|---|

BCPD-OFF | 6 | 5 | 0 | 0.545 | 1 | 0.706 |

BCPD-ON | 6 | 1 | 0 | 0.857 | 1 | 0.923 |

BCPD-OFF-MV | 5 | 8 | 1 | 0.385 | 0.833 | 0.526 |

BCPD-ON-MV | 6 | 12 | 0 | 0.333 | 1 | 0.5 |

Robertson (2009) | 6 | 18 | 0 | 0.25 | 1 | 0.4 |

Method | Time Taken Per CPT Location (s) |
---|---|

BCPD-OFF | 2.46 |

BCPD-ON | 0.044 |

BCPD-OFF-MV | 3.32 |

BCPD-ON-MV | 2.38 |

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**MDPI and ACS Style**

Suryasentana, S.K.; Sheil, B.B.; Lawler, M.
Assessment of Bayesian Changepoint Detection Methods for Soil Layering Identification Using Cone Penetration Test Data. *Geotechnics* **2024**, *4*, 382-398.
https://doi.org/10.3390/geotechnics4020021

**AMA Style**

Suryasentana SK, Sheil BB, Lawler M.
Assessment of Bayesian Changepoint Detection Methods for Soil Layering Identification Using Cone Penetration Test Data. *Geotechnics*. 2024; 4(2):382-398.
https://doi.org/10.3390/geotechnics4020021

**Chicago/Turabian Style**

Suryasentana, Stephen K., Brian B. Sheil, and Myles Lawler.
2024. "Assessment of Bayesian Changepoint Detection Methods for Soil Layering Identification Using Cone Penetration Test Data" *Geotechnics* 4, no. 2: 382-398.
https://doi.org/10.3390/geotechnics4020021